Internal problem ID [7460]
Book: Second order enumerated odes
Section: section 2
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y=2 x^{3}-x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+3*y(x)=2*x^3-x^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x \left (2 x^{2} \ln \left (x \right )+\left (c_{1} -1\right ) x^{2}+2 x +2 c_{2} \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 27
DSolve[x^2*y''[x]-3*x*y'[x]+3*y[x]==2*x^3-x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \left (x^2 \log (x)+\left (-\frac {1}{2}+c_2\right ) x^2+x+c_1\right ) \]